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What is the Poisson distribution used to model?
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The Poisson distribution is used to model the number of events occurring within a given time interval.

The formula for the Poisson probability mass function is $p(x ; \lambda)=\frac{e^{-\lambda} \lambda^x}{x !}$ for $x=0,1,2, \cdots$
$\lambda$ is the shape parameter which indicates the average number of events in the given time interval.
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